Question: Rewrite as a simplified fraction. ${3.4\overline{6} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 346.6666...\\ 10x &= 34.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 312}$ ${x = \dfrac{312}{90}} $ ${x = \dfrac{52}{15}} \text{or} {3 \dfrac{7}{15}}$